Tangent-3 at the NTCIR-12 MathIR Task

We present the math-aware search engine Tangent-3 and report its results for the NTCIR-12 MathIR task. Tangent uses a federated search over two indices: 1) a TF-IDF textual search engine (Solr), and 2) a query-by-expression engine. We use an inverted index to store math expressions using pairs of symbols extracted from a Symbol Layout Tree representation built from Presentation MathML. We use a cascade model with two stages for retrieval. In the first stage, relevant expressions are retrieved quickly using iterator trees over posting lists to find matches and expressions are ranked using the Dice coefficient of matched symbol pairs. In the second stage, the top-k best candidates are reranked with a more strict similarity metric supporting unification and wildcard matching. Our system produces relevant (and partially relevant) Precision@5 values of 21% (50%) for the main arXiv task, 25% (49%) for the Main Wikipedia subtask and 45% (84%) for the Wikipedia Formula Browsing subtask.